JEE Main2026Apr 6, Shift 2

JEE Main 2026 — Apr 6, Shift 2

75 questions with step-by-step solutions. All free.

Mathematics

Q1Let $f : R \to R$ be defined as $f (x) = \frac{2 x ^{2} - 3 x + 2}{3 x ^{2} + x + 3}$ . Then $f$ is:
Q2 Consider the quadratic equation $(n^{2} - 2 n + \dots$
Q3Let $S = {z \in C : z^{2} + 6 i z - 3 = 0}$ . Then $z \in S \sum z^{8}$ is equal to:
Q4 The sum of all possible values of $θ \in [0, 2 π]$ , for which the system of equations: $x cos \dots$
Q5Let $A = 100310931$ and $B = [b_{ij}]$ , $1 \leq i, j \leq 3$ . If $B = A^{99} - I$ , then the value of $\frac{b _{31} - b _{21}}{b _{32}}$ is:
Q6The sum $1 + \frac{1}{2} (1^{2} + 2^{2}) + \frac{1}{3} (1^{2} + 2^{2} + 3^{2}) + \dots$ upto 10 terms is equal to:
Q7 A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to: …
Q8 Let the mean and the variance of seven observations $2, 4, α, 8, β, 12, 14$ , $\alpha …
Q9 A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is: …
Q10 Let $C$ be a circle having centre in the first quadrant and touching the $x$ -axis at a distance 3 units from the origin. If the circle $C$ has an intercept of length $6 \dots$
Q11 The eccentricity of an ellipse $E$ with centre at the origin $O$ is $2 \dots$
Q12 Let $x = 9$ be a directrix of an ellipse $E$ , whose centre is at the origin and eccentricity is $\dots$
Q13If $sin (tan^{- 1} (x 2)) = cot (sin^{- 1} 1 - x^{2})$ , $x \in (0, 1)$ , then the value of $x$ is:
Q14The shortest distance between the lines $\frac{x - 4}{1} = \frac{y - 3}{2} = \frac{z - 2}{- 3}$ and $\frac{x + 2}{2} = \frac{y - 6}{4} = \frac{z - 5}{- 5}$ is:
Q15 Let $a = 2 \dots$
Q16 Let $x \to 2 lim \dots$
Q17 Let $A = \dots$
Q18 Let $f : R \to R$ be such that $f (x \dots$
Q19The area of the region ${(x, y) : x^{2} - 8 x \leq y \leq - x}$ is:
Q20The value of the integral $\int_{- 1}^{1} (\frac{x ^{3} + ∣ x ∣ + 1}{x ^{2} + 2∣ x ∣ + 1}) d x$ is equal to:
Q21Let $R = {(x, y) \in N \times N : lo g_{e} (x + y) \leq 2}$ . Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is _____.
Q22If $(1 - x^{3})^{10} = r = 0 \sum 10 a_{r} x^{r} (1 - x)^{30 - 2 r}$ , then $\frac{9 a _{9}}{a _{10}}$ is equal to ______.
Q23 Let the line $x - y = 4$ intersect the circle $C : \dots$
Q24 Let the image of the point $P (0, - 5, 0)$ in the line $2 \dots$
Q25 Let $f(x) = \begin{cases} x^{3} + 8, & x …

JEE Main 2026 — Apr 6, Shift 2

Mathematics

Physics

Chemistry

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